A study of changes in the transmission of a disease, in particular, a new disease like COVID-19, requires very flexible models which can capture, among others, the effects of non-pharmacological and pharmacological measures, changes in population behaviour and random events. We favour data-driven approaches over a priori and ad-hoc methods and introduce a generalised family of epidemiologically informed mechanistic models, guided by Ordinary Differential Equations and embedded in a probabilistic model. The mechanistic models SIKR and SEMIKR which divide the population into disjoint compartments for individuals Susceptible to infection, Infectious (K sub-compartments), Exposed (M sub-compartments), and Removed from the pool of susceptible are enriched with a time-dependent transmission rate, parameterised using Bayesian P-splines. Such a parameterisation enables an extensive flexibility in the transmission dynamics, without resorting to ad-hoc specifications. Our probabilistic model relies on the solutions of a mechanistic model and benefits from access to the information about under-reporting of new infected cases, a crucial property when studying diseases with a large fraction of asymptomatic infections. Such a model can be differentiated efficiently, which makes Hamiltonian-based Monte Carlo sampling feasible after a careful initialisation and tuning strategy. This is particularly important in the present setting with weakly identified directions and challenging posterior geometries. Furthermore, we apply our methodology to study the transmission dynamics of COVID-19 in the Basque Country (Spain) from mid February 2020 to the end of January 2021, showing how the framework can recover plausible temporal patterns in transmission while making explicit the dependence of the results on modelling choices and convergence diagnostics.

翻译：对疾病传播变化的研究，特别是像COVID-19这样的新型疾病，需要极为灵活的模型来捕捉非药物与药物干预措施、人群行为变化及随机事件等效应。我们优先采用数据驱动方法而非先验或特设方法，引入一个基于常微分方程指导并嵌入概率模型的广义流行病学机理模型族。将人群划分为易感者、感染者（K个子室）、暴露者（M个子室）及移除者等不相交室间的机理模型SIKR和SEMIKR，通过贝叶斯P样条参数化的时变传播率得到增强。该参数化方法无需特设规范即可实现传播动力学的高度灵活性。我们的概率模型基于机理模型的解，并能利用新感染病例漏报信息——这对研究无症状感染比例较高的疾病至关重要。该模型可高效求导，在精心初始化和调参策略后，使得基于哈密顿的蒙特卡洛采样可行，尤其适用于弱识别方向和具有挑战性的后验几何结构场景。此外，我们应用该方法研究了2020年2月中旬至2021年1月底西班牙巴斯克地区的COVID-19传播动力学，展示了框架如何恢复传播的合理时序模式，同时明确结果对建模选择和收敛诊断的依赖性。